2. Trigonometric Functions on Right Triangles

Mary thinks the triangle is equilateral. How would you support or dispute her conjecture using trigonometric functions on right triangles?

In a right triangle, if point A is at $(3,2)$ and point B is at $(3,7)$, what is the vertical change from point A to point B?

$\text{If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are:}$

Given a right triangle where side $LK$ is $7$ units, side $KJ$ is $24$ units, and $LJ$ is the hypotenuse, what is the measure of angle $LKJ$? Round to the nearest whole degree.

In the context of right triangles and their angles, which term best describes a pair of angles that are both $\mathrm{vertical}$ and $\mathrm{supplementary}$?

Given that a transversal cuts two parallel lines and forms angles such that $m\angle 4$ = $55.1°$, what are the measures of $m\angle 5$ and $m\angle 7$?

Given a right triangle where one of the acute angles is $x$ and the lengths of the sides opposite and adjacent to $x$ are $3$ and $4$ respectively, what is the value of $x$ in degrees?

In a right triangle, if the length of the adjacent side to angle $x$ is $5$ units and the hypotenuse is $13$ units, what is the value of $\cos \left(x\right)$?

Given a right triangle with hypotenuse of length $c$ and an acute angle $\theta$, express the lengths of the side adjacent to $\theta$ (labeled $a$) and the side opposite $\theta$ (labeled $b$) in terms of $c$ and $\theta$.

In a right triangle, if the length of the adjacent side is $1$ and the length of the opposite side is $\sqrt{3}$, what is the measure of the angle (in degrees) opposite the side of length $\sqrt{3}$?

In circle O, if arc AB measures $48°$, what is the measure of angle CAB, where C is a point on the circle such that angle CAB is an inscribed angle that intercepts arc AB?

Given a right triangle with angle $\mathrm{FGE}$ and the side opposite to $\mathrm{FGE}$ has length $a$, the side adjacent to $\mathrm{FGE}$ has length $b$, and the hypotenuse has length $c$, which equation can be used to find the measure of angle $\mathrm{FGE}$?

In right triangle $PQR$, if angle $Q$ is the right angle, side $PQ$ = $7$ and side $QR$ = $8$, what is the measure of angle $R$? Round to the nearest degree.

In right triangle $△PQR$, the angle bisector of $\angle PQR$ is $QE$. If $m\angle PQE=20°$, what is the measure of $\angle PQR$?

Given a right triangle EGF with $\angle G$ as the right angle, if the side opposite $\angle E$ is $7$ units and the side adjacent to $\angle E$ is $9$ units, which is the best approximation for the measure of $\angle EGF$?